J . Phys. Chem. 1993,97, 6598-6601
6598
Adhesion of AgI Molecules to Gaseous Metallic Silver Cluster Cations Clifton K. Fagerquist, Dilip K. Sensharma, Temer S. Ahmadi, and M. A. El-Sayed’ Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90024 Received: February 18, I993
The evaporative channels for the unimolecular dissociation of metastable AgxIy+ (X= 5-25; Y = 0-4)clusters made by fast atom bombardment of silver foil in the presence of CH31vapor are observed in the first field-free region of a double-focusing mass spectrometer. We found three dominant neutral evaporative channels: Ag loss, Ag2 loss, and AgI loss. Only Agl2I3+ is found to have an additional channel involving an (AgI)3 loss. Consistent with our previous studies of stable Ag&+ clusters, we assume a structural formula of (A&-y)+(AgI)y, where the metallic part of the cluster conforms to Jellium model predictions. In comparing the relative evaporative loss of AgI from these metastable clusters, we observe: (a) evidence for significant AgI-AgI interaction for clusters whose metallic part has a 1s2, lp2, or ls21p4Jellium configuration; (b) a near constant fractional loss of AgI as the number of AgI units in the parent cluster increases for clusters whose metallic part has a closed main Jellium shell; (c) a relative increase in the fraction loss of AgI as the number of AgI molecules in the parent cluster increases for clusters with an “open”-shell configuration for the metallic part. These observations are discussed in terms of evaporative loss of AgI from structures in which the AgI molecules solvate the metallic part of the cluster. It is proposed that the heat of AgI evaporation is greatly determined by dipole/induceddipole interactions between the permanent dipole of AgI and the polarizable delocalized electron density of the metallic part of the cluster.
Introduction The Jellium model is found to account for the relative stability and observed structural propertiesfor alkali-lJ and noble-metal)~~ clusters and to a certain extent other metallic clusters as well.5 Clusters with a number of metallic valence electronscorresponding to a main Jellium shell closing (8, 20, 34,40, etc.) are found to have extra stability over those with one electron in excess, which tend to lose the extra valence electron through atom evaporation to attain a closed-shell configuration. According to the Jellium mode1,6.7 main shell closings are predicted at the electronic configurations: ls2lp6 (eight electrons); ls2lp61d102sZ (20 electrons); ls21p61d”J2szlP4(34 electrons), etc. The binding and the stability in alkali halide clusters and their cations have been discussed in terms of the polarizable ion model.889 Increased stability is obtained for clusters with maximum interaction between the metal cations and halide anions. The formation of lattices with an odd integer number of ions on each of its three edges are found to have extra stability as compared to those with one more MX unit. Studies of “mixed”metallic/ionic clusters for the alkali metals have been carried out for C S / C S Z Oand ~ ~ Na/NaC1ll clusters. Whetten and co-workers have estimated the binding energy of an excess electron in slightly metal-rich alkali halide clusters12 as well as metallization of purely ionic clusters by photoinduced ejection of halogen atoms.” Rabin et al.14 have generated nonstoichiometric metal-rich AgF clusters by inert aggregation technique. From their relative mass intensities they have suggested a cluster structurecomposed of a metallic “core”encased in a “shell” of fluorine anions. In our previous work,ls we partially converted silver clusters to “mixed”silver/silver iodide clusters by fast atom bombardment (FAB) sputtering of silver foil in the presence of methyl iodide vapor. In that work, we studied both positively and negatively charged silver/silver iodide clusters having one to four AgI units in the cluster. For clusters of composition AgxIy(+/-),we found the Jellium model to explain relative intensities of the observed mass spectra. We also observed a correlation between our collision-induced dissociation results of Agy(Ag1) clusters16with the measured electron affinities of the neutral silver clusters by other groups.17 Our results are consistent with the Jellium model 0022-365419312097-6598504.00/0
only if one assumes that these clusters have a structural formula of the type (Agx-y)(+/-)(AgI)ywherethe charge resides primarily on the metallic part of the cluster. In the present work, we wish to understand the binding of the AgI unit@)in metastable (Agx-y)+(AgI)yclustersfor X = 5-25 and Y = 1-4. Do the AgI molecules nucleate into an ionic lattice that is attached to the metallic part of the cluster or do the AgI dipolar molecules “solvate”the metallic cluster cations? In order to answer this question, we have determined the relative evaporation probability of AgI loss from metastable AgxIy+ clusters that have “open” and “closed”Jellium shell configurations for the metallic part of the cluster. We have used a “linked” mass spectrometry scanning technique to determine the fractional evaporative loss of Ag, Agz, and AgI from these metastable clusters. In addition, we observed for one particularAgxIy+cluster a unique dissociative loss, which not only supports the structural formula (Agx-y)(+/-)(AgI)ybut also suggests the conditions for which ionic lattice formation are favorable. The observed results are discussed in terms of competitive dipoleldipole vs dipole/ induced-dipole forces as they effect ionic lattice formation vs dipole solvation of the metallic part of the cluster. We also propose that the adhesion energy of the evaporating AgI molecule is determined, for most of the clusters studied here, by interactions between the permanent dipole moment of the AgI molecule and the static polarizability of the Jellium electrons of (A&-,,)+ modified by the effect, if any, of the dipole moments of the Y 1 AgI molecules remaining on the cluster. The reorganization energy of the Jellium electrons of (Agx-y)+ after loss of an AgI may also contribute to the heat of evaporation of an AgI. Experimental Section
The experimental setup was described in a previous paper.15 Briefly, the instrument used in our experiments is a VG Analytical ZAB-70 SE double-focusing mass spectrometer (“reverse” geometry) fitted with a fast atom bombardment gun (Model FABl l N , Ion Tech Ltd., Teddington, Middlesex, UK). Isotcpically enriched silver foil that is 98.54% Io7Ag,of dimensions 3 mm X 10 mm, was mounted on a FAB probe tip and inserted into the source region. 0 1993 American Chemical Society
Adhesion of AgI Molecules
The Journal of Physical Chemistry, Vol. 97, No. 25, 1993 6599
0
1
2
3
4
Y S O
1
2
3
4
1
0
2
3
4
h
8-
v
v)
Q,
C C
m
5 C
0 .c
20
a m >
W
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> .-+
-ma
U Figure 1. Relative evaporative channels for selected metastable cluster
ions whose metallic part is smaller than the eight-electron Jellium shell closing. The electronic configuration of the metallic part of the parent cluster ion is given in each display. Ydenotes the number of AgI molecules of the parent cluster ion. The foil was sputtered with the FAB gun typically at 7.0 kV with a discharge current of 1.4 mA. Methyl iodide vapor was introduced into the source region from a heated diffusion port at a temperature of 100 OC. The methyl iodide vapor effusing out of the diffusion port forms a vapor jet, part of which is directed toward the sputtered silver foil, although the methyl iodide is dispersed generally throughout the entire chamber. Upon introduction of the methyl iodide, the base pressure in the source region increased from (5.0-7.0) X lo” mBar (xenon FAB gas) to (2-3) X le5 mBar as read continuouslyduring the experiment from an ion guage located above the source chamber diffusion pump. The unimolecular dissociationof metastable cluster ions in the first field-free region (1st FFR) of this instrument was studied by using a “linked” scanning technique: constant neutral mass loss mass spectrometry (CNML-MS).18J9 CNML mass spectrometry, which will be discussedin greater detail in a forthcoming paper,2O involves scanning both the magnetic and electric sectors simultaneously such that the strength of the magnetic to electric fields is maintained at a fixed mathematical ratio, corresponding to a specified neutral mass loss. CNML-MS scanning detects all metastable ions that dissociateby evaporative loss of a specified neutral. With only one unique exception, we detected three evaporativechannels for the unimolecular dissociation of AgxIy+ clusters in the 1st FFR of our instrument: Ag loss, Agz loss, and AgI loss.
20
........... Y:O
...-..._._. Q
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2
3
4 4
Figure 2. Relative evaporative channels for selected metastable cluster
ions whose metallic part has a closed Jellium shell. The electronic configurationof the metallic part of theparent cluster ion is given in each display. Y denotes the number of AgI molecules of the parent cluster ion. 0
1
2
3
4
Y Z O
1
2
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4
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Results and Discussion We are concerned with the relative binding of AgI unit(s) in metastable AgxIy+ clusters. We have observed that for AgxIy+ clusters that have an oddnumber of delocalizedvalence electrons in their metallic parts, dissociation occurs almost exclusively by metallic monomer loss. The dominance of metallic monomer loss from odd-electron alkali- and noble-metal clusters has long been observed experimentallyZ1J2and discussed in terms of the Jellium model. The presence of the AgI molecules does not seem to alter the dominance of Ag monomer loss for these odd-electron clusters, suggesting that the integrity of the metallic part is not greatly changed by the presence of the few AgI molecules in the “mixed” clusters we presently examine. In order to study the evaporative loss of AgI, we were forced to limit our study to the evaporative losses from ‘mixed” clusters whose metallic part has an euen number of metallic valence electrons. The important observations are shown in Figures 1-3 and are
Figure 3. Relative evaporative channels for selected metastable cluster
ions whose metallic part has an open Jellium shell closing. The electronic configurationof the metallic part of theparent cluster ion is given in each display. Y denotes the number of AgI molecules of the parent cluster ion. described below, The error bars in the figures indicate the standard deviation in a branching ratio for three separate experiments taken on three different days.
6600 The Journal of Physical Chemistry, Vol. 97, NO. 25, 199'3 1. Figure 1 shows the relative evaporation probability of the three neutral evaporative channels as a function of the number of AgI molecules (Y)in the parent cluster ions where the metallic part has less than eight valence electrons (Le., small cluster size). The Jellium electronic configuration of the metallic part of the parent cluster ion is indicated in each figure. For the purpose of comparison, the dissociation pattern for purely metallic cluster ions is shown at the far left of each figure (Y = 0). The most important observation in Figure 1 is the drastic decrease in the relative evaporation probability of AgI as a second AgI is added to the parent cluster. Such a decrease becomes less evident either as more AgI is added (Y increases from 2 to 4) or as the size of the metallic part increases: top to bottom display. Upon completion of the metallic ls21p6 Jellium shell (top display in Figure 2) the "dip" for two AgI is totally absent. 2. Figure 2 shows the relative evaporation probability of the neutral evaporative channels for metastable clusters that have a closed Jellium shell in their metallic part. For the ls21p6series (top display), we observe a relatively constant loss of AgI except for Y = 3 (Ag1213+). The strong dissociative loss of three AgI from Ag1213+is unique among the metastable Ag# clusters studied here. No other metastable AgxIu+ clusters were observed to unimolecularly dissociate via three AgI loss. Although AgI loss from the ls21p61d102s2 series (bottom display) is not as dominant as for the ls21p6, it is relatively constant except for a noticeabledropat Y =4. The ls21p61d1°series (middledisplay), which is not a main shell closing, shows a noticeable rise in AgI loss intensity with greater numbers of AgI in the parent cluster until we observe a drop for Y = 4. 3. Figure 3 shows the relative evaporation probability of the three neutral evaporative channels for metastable clusters that have an open Jellium shell in the metallic part of the parent cluster. For these clusters, we observe a steady increase in the relative probability of AgI loss and/or a steady decrease in the relative probability of the metallic monomer and dimer loss. Since the latter two have similar negative slopes, one is tempted to explain the observed trend to result from an increase in the evaporation probability of AgI loss as the number of AgI in the parent cluster increases. The above results can be summarized as follows: ( 1) for clusters whose metallic part is below the ls2lp6 Jellium shell closing (Le., for relatively small clusters), the addition of a secondAgI molecule to the parent cluster is found to reduce significantly the probability for evaporative loss of AgI; further addition of AgI molecules is found to help recover the reduction in theevaporation probability; (2) for clusters whose metallic part has a closed main Jellium shell, the evaporation probability for AgI loss appears to be independent of the number of AgI molecules present in the cluster (theonly exception being Agl*I3+);(3) for clusters whose metallic part has an open Jellium shell, there is a general increase in the relative evaporation probability of an AgI molecule as the number of AgI remaining on the cluster increases. Heat of Evaporation of an AgI Molecule. These observations might be understood as follows. If we assume that AgI molecules evaporate from a structure in which the AgI molecules solvate the metallic part of the cluster and the AgI ionic bond does not significantly change in strength upon evaporation, one can derive for the heat of evaporation of an AgI molecule from a "mixed" cluster the following expression: MA~Ie w
-- AHAgI-lAg~~-,+l.(AgO~-,4- mGW-AgO, AH1
+Mreog = + A H 2 + A H 3 (1)
where A H 1 is the interaction energy between the permanent dipole of the evaporating AgI molecule and the induced dipole of the metallic part of the cluster. A H 2 is the dipole-dipole interaction energy between the evaporating AgI molecule and any other AgI molecules remaining on the cluster. AH3 is an electronic reorganization energy resulting from the changes in the delo-
Fagerquist et al. calization energy of the electrons in the metallic part of thecluster upon AgI evaporation. A H 1 and A H 2 are positive quantities. AH3 is negative due to the fact that the evaporation of an AgI molecule should lead to greater electron delocalization and an increase in the static polarizability of the metallic part of the cluster. Greater electron delocalization of the metallic electrons upon loss of an AgI molecule is consistent with the idea that the ionic unit(s) act to confine the metallic electron density-as suggested by Martin et a1.I0to account for the observed decrease in the ionization energy of the Csx(Cs2O)yclusters as the number of ionic units is increased. Since both AH1 (and partly AH3) terms involve interactions between the AgI dipoles and thestaticpolarizabilityof themetallic part of the cluster, a knowledge of the static polarizabilities of Agx+ clusters is needed. These numbers are not presently available. However, results on the static polarizabilities of neutral alkali clusters23and more recently the giant absorption resonances for Agx+ clusters have become available.24 These studies suggest that the static polarizability drops at main Jellium shell closings relative to the polarizability of neighboring open-shell clusters. We outline below how competing dipole/dipolevs dipole/induceddipole forces may account for our evaporation observations. Observation 1 can be explained as follows. In the smallest clusters, the absolute static polarizability of the metallic part is relatively small, leading to a small AHl. In addition, the distance between the AgI dipoles is relative small, thus increasing the relative importance of the A H 2 term. These two facts thus lead to the conclusion that the A H 2 term dominates over AH1 in these clusters. The largest effect on A H ~ I is expected upon changing Y from 1 to 2, where AH2 changes from 0 to a nonvanishing value. The recovery of the relative evaporation of AgI for Y = 3 and 4 may be due to weak trimer and tetramer structures of AgI and/or steric "blocking" of metallic dissociation channels by a surrounding "shell" of AgI molecules. Observation 2 suggest relatively weak dipols-dipole interactions (AH2)for Y = 2,3,4. The fact that the addition of a second AgI does not decrease the evaporation probability suggests that the AgI-AgI interaction is not dominant in determining the AHcvpp of AgI molecules from clusters with 2, 3, or 4 AgI units. One explanation of this could be that clusters with 2,3, or 4 AgI units do not nucleate into stable ionic geometries but rather solvate the Agx+cluster. An apparent exception is the dissociation of AB&+, which will be discussed later. For the 18 and 20 electron shell closing, the dipole/dipole separation could be sufficiently large to reduce the interaction energy below that resulting fromdipole/ induced dipole. The high internal energies of metastable clusters may also favor dipole/induced-dipole forces over dipole-dipole. The fact that the addition of AgI molecules enhances, rather than diminishes, the AgI evaporation probability (observation 3) gives the strongest evidence that AgI evaporation takes place from solvated "mixed" clusters rather than from an (AgI) *lattice. The observed enhancement can be explained by the expected decrease in the static polarizability of the metallic part of the cluster as the number of AgI in the parent cluster increases. This takes place as a result of the localization of the metallic Jellium electrons by the dipolar forces of the added AgI molecules. A decline in the static polarizability would in turn lead to a decrease in AH1 (dipole/induced-dipole forces), which would lead to a decrease in A H ~cvap I and thus to an enhancement of the AgI evaporation channel. While our results support the idea of solvation for most of the clusters observed here, one has to realize that the origin of the change in the relative evaporation probability of one channel, as the number of AgI molecules increase, can result from a change in the relative evaporation probability of any of the other two dissociation channels. However, it is difficult to explain why the loss of Ag or Ag2 would be enhanced as we add one more AgI molecule to a cluster that already has one AgI molecule.
Adhesion of AgI Molecules Another important point needs to be mentioned. In our comparisons, we are assuming that the “temperature” of these metastable clusters is not very different from one another and that the evaporation is statistical. The success of the evaporative ensemble modeP-27 in describingobservationson the evaporation from different types of clusters is based on statistical evaporation dynamics. Dissociative Loss of Thee AgI Molecules from Ag&+. Ag124+ was the only cluster observed to evaporate three AgI molecules in addition to Ag, Ag2, and AgI. There are three possible evaporativechannels for dissociative loss of three AgI: (1) direct “fission” of Ag&+ into Agg+ and (AgI)3; (2) sequential loss of AgI and (AgI)2; (3) sequential loss of three AgI molecules. The latter two routes, although possible, are statistically unlikely. Statistical evaporation dynamics would tend to favor direct “fissionn over sequential evaporative loss.28 More significantly, if sequential evaporation were present, we should have observed some evaporative loss of two AgI from Ag&+. In fact, we do not observe any loss of two AgI from Ag1213+.In addition, the recent observation29 of a strong AgI trimer loss channel from purely ionic AgI clusters suggests that (AgI)3is a stable species and thus supports the importance of this channel in our study. Thus, we conclude that theformation of (AgI)3 in Agl2Ip+occurs prior to “fissionn of the metallic and ionic parts of the cluster. The question arises as to why Ag&+ is the only cluster found to have an (AgI)3 evaporative channel. There are two possible reasons. (1) The daughter ion formed, Agg+, has a main Jellium shell closing, which gives it unusual stability.
(2) In addition, Agg+ also has a low static polarizability due to its Jellium closed shell. A low static polarizability for the metallic part of the cluster may result in unusually weak dipole/induceddipole forces. Weak dipole/induced-dipole forces, in turn, may facilitate AgI lattice nucleation as a prelude to metallic/ionic “fission”. However, it is impossible for us to know for how long prior to dissociation the AgI trimer exists. As mentioned previously, the stability of (AgI)3was recently29 suggested by the detection of (AgI)3 loss as a major evaporative channel of metastable [Ag(AgI),+] clusters. Early spectroscopic work on silver chloride and silver bromide clusters in rare-gas matrices concluded that the trimer geometry of these clusters is a distorted hexagonal ring.30 It is not yet known whether (AgI)3 also has hexagonal ring structure. The absence of (AgI)3 loss from any other clusters (including the next main Jellium closed shell, Ag21+(AgI)3,,4) may be due to the increased static polarizability of the metallic part. Dipole/ induced-dipole forces between the AgI dipoles and the larger polarizable metallic part may slow down the diffusion of the AgI units toward one another. This together with the larger volume of the cluster may slow down lattice formation (and dissociative loss) compared to cluster decomposition via other dissociative channels. W h y Solvated Structure? Why does the solvated structure appear to predominate for these metastable clusters rather than a structuremadeof a strong ionic lattice interacting with a metallic part of the cluster? Several factors may contribute: (1) AgI has a relatively weak ionic dipole-the highest estimated value 5.95 D.31 By comparison, CsI has a dipole moment of 11.69 D.32 AgI lattice formation would be significantly weaker compared with the that of alkali halides. (2) Metastable clusters, by their very nature, have high internal energies. Dipole/dipole alignment (a prerequisitefor lattice formation) may be thwarted by competitive dipole/induced-dipole forces at the high internal energiesof these metastable clusters. (3) Entropic effects may also favor a random distribution and orientation of dipoles. (4) The clusters studied here are made by sputtering silver foil in the presence of methyl iodide vapor. It is possible that the solvated-type clusters are
The Journal of Physical Chemistry, Vol. 97, No. 25, 1993 6601 kinetically favored because of the method of preparation. ( 5 ) It
is also possible that for the larger clusters we may have a number of isomers with AgI molecules “inside” the cluster as monomer, dimer, or trimer units as well as AgI attached to the “surface”. Surface AgI would have a higher evaporation probability. (6) It is also possibiethat for the small number of AgI units a solvated structure is thermodynamically favored. If greater number AgI units are added (Y> 4), the AgI lattice energy might finally overcome the dipole/induced-dipole forces as well as the entropic factors to induce phase separation! In conclusion, for these electronically “mixed” metastable clusters, we propose a structure wherein the polarizable metallic electron density is solvated by the permanent dipoles of AgI molecules. We suggest that the lower polarizability of clusters whose metallic part has a closed spherical Jellium shell results in a constant evaporative loss of AgI from the cluster (unless ionic lattice formation occurs, as in the case of Ag1213+).On the other hand, for clusters whose metallic part has an open Jellium shell, we suggest that the successive addition of AgI molecules results in a decrease of the polarizability of the metallic electrons and thus the binding (and activation energy) of the evaporating AgI molecule from these clusters. Acknowledgment. We thank the support of the Office of Naval Research (Contract N00014-89-J- 1350). References and Notes (1) deH~,W.A.;Knight,M.Y.Chou;Cohen,M.L.SolfdStatePhys. 1987, 40, 93. (2) Cohen, M. L.; Chou, M. Y.; Knight, W. D.; de Heer, W. A. J. Chem. Phys. 1987, 91, 3141. (3) Katakuse, I.; Ichihara, T.; Fujita, Y.; Matsuo, T.; Sakurai, T.; Matsuda, H. In?.J . Mass Spectrom. Ion Proc. 1985,67,229; 1986, 74,33. (4) Katakuse, I.; Ichihara, T.; Fujita, Y.; Matuso, T.; Sakurai, T.; Matsuda, H. In?. J. Mass Spectrom. Ion Proc. 1986, 69, 109. (5) Begemann, W.; Mciwcs-Broer K. H.; Lutz, H. 0. Phys. Rev. Lett. 1986, 56, 2248. (6) Penzar, Z.; Ekardt, W. 2.Phys. D-At., Mol., Clusters 1991, 19, 109. (7) Ekardt, W. Phys. Rev. B 1984, 29, 1558. (8) Diefenbach, J.; Martin, T. P. J . Chem. Phys. 1985, 83, 4585. (9) Martin, T. P. Phys. Rep. 1983, 95, 167. (10) Bergmann, T.; Martin, T. P. J. Chem. Phys. 1989, 90,2848. (1 1) Pollack, S.; Wang, C. R. C.; Kappes, M. M. Z . Phys. D At., Mol., Clusters 1989, 12, 241. (12) Honea,E.C.;Homer,M. L.;Labastie,P.; Whctten,R.L. Phys. Rev. Lett. 1989, 63, 394. (13) Li, X.; Beck, R. D.; Whetten, R. L. Phys. Rev. Lett. 1992,68,3420. (14) Rabin, I.; Schulze, W.; Ertl, G. Z . Phys. Chem. N.Folge 1990,169, 85. (1 5 ) Fagerquist, C. K.;Sensharma,D. K.;El-Sayed, M. A. J. Phys. Chem. 1991, 95, 9169. (16) Fagerquist, C. K.;Sensharma,D. K.; El-Sayed, M. A.J. Phys. Chem. 1991, 95, 9176. (17) Ho, K.; Ervin, K. E.; Lineberger, W. C. J . Chem. Phys. 1990, 93, 6987. (18) Haddon, W. F. Org. Mass.Spectrosc. 1980. (19) Zakett, D.; Schoen, A. E.; Kondrat, R. W.; Cooks, R. G. J. Am. Chem. SOC.1979, 101,6781. (20) Fagerquist, C. K.; Sensharma, D. K.; El-Sayed, M. A. J . Phys. Chem.,
to be submitted. (21) Brechignac, C.; Chauzac, Ph.; Carlier, F.; de Frutos, M.; Leygnier, J. J . Chem. Soc., Faraday Trans. 1990,86,2525. Brechignac, C.; Cahuzac, Ph.; Leygnier, J.; Weiner, J. J. Chem. Phys. 1989, 90,1492. (22) Begemann, W.; Meiwes-Broer, K. H.; Lutz, H. 0.Phys. Rev. Lett. 1986,56,2248. Begemann, W.; Dreihofer, S.;Meiwes-Broer, K. H.; Lutz, H. 0. 2.Phys. D - A t . , Mol. Clusters 1986, 3, 183. (23) Knight, W. D.; Clcmenger, K.; de Heer, W. A,; Saunders, W. A. Phys. Rev. B 1985, 31, 2539. (24) Tiggeabaumker, J.; Koller, L.; Lutz, H. 0.; Meiwes-Broer, K. H. Chem. Phys. Lett. 1992,190,42. (25) Klots, C. E. J. Chem. Phys. 1985,83, 5854. (26) Klots, C. E. 2.Phys. D 1987, 5.83. (27) Klots, C. E. J. Phys. Chem. 1988, 92,5864. (28) Hwang, H. J.;Sensharma, D. K.; El-Sayed, M. A. Chem. Phys. Lett. 1989, 160, 243. (29) Jerger, T.; Kreislc, D.; Recknagel, E. ISSPIC Confcence-Chfcago ’92. Jerger, T.; Kreisle, D.; Recknagel, E. Z . Phys. D, in press. (30) Martin, T. P.; Schaber, H. J. J. Chem. Phys. 1980, 73, 3541. (31) Singh, I. B.; Rai, S B. Ind. J . Phys. 1990,64B, 386. (32) Story Jr., T.L.; Hebert, A. J. J. Chem. Phys. 1976,64,855.
